Time-dependent bifurcation: A new method and applications

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 12, 2001, Pages 3153-3162

  Hua, Cun Cai ^a   Lu, Qi Shao ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035652955     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401004091     Document Type: Article

References (21)

1. Baer, S. M., Erneux, T. & Rinzel, J. [1989] "The slow passage through a Hopf bifurcation: Delay, memory effects and resonance," SIAM J. Appl. Math. 49(1), 55-71.
2. Erneux, T. & Mandel, P. [1983] "Temporal aspects of absorptive optical bistability," Phys. Rev. A28(2), 896-909.
3. Erneux, T. & Mandel, P. [1984] "Stationary, harmonic and pulsed operations of an optically bistable laser with saturable absorber. II," Phys. Rev. A30(4), 1902-1909.
4. Erneux, T. & Mandel, P. [1986] "Imperfect bifurcation with a slowly-varying control parameter," SIAM J. Appl. Math. 46(1), 1-15.
5. Erneux, T. & Laplante, J. P. [1989] "Jump transition due to a time-dependent bifurcation parameter in the bistable iodate-arsenous acid reaction," J. Chem. Phys. 90(11), 6120-6134.
6. Erneux, T. & Mandel, P. [1989] "Slow passage through the laser first threshold," Phys. Rev. A39(10), 5179-5188.
7. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
8. Harberman, R. [1979] "Slowly varying jump and transition phenomena associated with algebraic bifurcation problems," SIAM J. Appl. Math. 37(1), 69-106.
9. Holden, L. & Erneux, T. [1993] "The slow passage through a Hopf bifurcation: From oscillatory to steady solutions," SIAM J. Appl. Math. 53(4), 1045-1058.
10. 3 = 0," Int. J. Nonlin. Mech. 15, 449-458.
11. Hua, C. C. & Lu, Q. S. [1999] "Bifurcation and optical bistability of Laser-Lorenz equation induced by the pump parameter slowly varying with time," Acta Phys. Sinica 40(8), 408-415 (in Chinese).
12. Hua, C. C. & Lu, Q. S. [2000] "Time-dependent bifurcation and dynamical behaviors of the absorptive optical bistability equation," Acta Phys. Sinica 41(4), 733-740 (in Chinese).
13. Laplante, J. P., Erneux, T. & Georgiou, M. [1991] "Jump transition due to a time-dependent bifurcation parameter: An experimental, numerical, and analytical study of the bistable iodate-arsenous acid reaction," J. Chem. Phys. 94, 371-378.
14. Mandel, P. & Erneux, T. [1984] "Laser-Lorenz equations with a time-dependent parameter," Phys. Rev. Lett. 53(19), 1818-1820.
15. Mandel, P. & Erneux, T. [1987] "The slow passage through a steady bifurcation: Delay and memory effects," J. Stat. Phys. 48(5/6), 1059-1070.
16. Maree, G. J. M. [1993] "Sudden change in a second-order nonlinear system with a slowly varying parameter," Int. J. Nonlin. Mech. 28(4), 406-426.
17. Maree, G. J. M. [1996] "Slow passage through a pitchfork bifurcation," SIAM. Appl. Math. 56(3), 889-918.
18. Raman, A., Bajaj, A. K. & Davies, P. [1996] "On the slow transition across instabilities in nonlinear dissipative systems," J. Sound Vibr. 192(4), 835-836.
19. Raman, A., Bajaj, A. K. & Davies, P. [1998] "On the non-stationary passage through bifurcation in resonantly forced Hamiltonian oscillators," Int. J. Nonlin. Mech. 33(5), 907-933.
20. Virgin, L. N. [1986] "Parametric studies of the dynamic evolution through a fold," J. Sound Vibr. 110(1), 99-109.
21. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, NY).